Help In understanding Rate Of Change in mm per sec

[tomtomtom1]

Hi everyone

Firstly this is not a homework question, i work in transport engineering. ( i do study part time which is why i sometimes post in the homework section)

Now to the problem.

I am trying to understand how to solve this problem, i already know the answer.

A train is traveling on straight & level track at 136.794kph.
It approaches a transition. The transition is 60m long.
Along the transition the Left Rail rises linearly over the length of the transition relative to the right Rail by 25mm.
Calculate the rate of change the left rail raises over the right in mm per sec over the 60m transition at 136.794kph.

i know that the answer is (25mm * 136.794kph) / (3.6 * 60m)

what i need help with is where does the 3.6 some from? and why do you times 25mm by 136.794kph?

can anyone explain

Thanks

 

[SteamKing]

The transition length is 60 m long. In this distance, the rails rise by 25 mm. Doesn't this suggest a slope?
The train is traveling at 136.794 km/hr. How do you convert 136.794 km/hr to a speed measured in m/s?

 

[tomtomtom1]

The transition length is 60 m long. In this distance, the rails rise by 25 mm. Doesn't this suggest a slope?

Yes there is a slope and the slope is 25mm/60m = 1m per 0.416mm which means for every 1m the train travels along the transition the left rail rises by 0.416mm.

The train is traveling at 136.794 km/hr. How do you convert 136.794 km/hr to a speed measured in m/s?

1kph = 0.277777778 m/s so 136.794km/hr in m/s is 136.794*0.277777778 = 37.998m/s.

 

[jacket]

rate of change the left rail raises = 25mm / (time needed to cross 60m)
= 25 mm / (60 m / velocity)
= 25 mm / (60 m / 136.794 km per hour)
Now, 1 km per hour = 1000 m / 3600 sec = 1/3.6 meter per sec
So,
rate of raise = 25 mm / (60 m / ((136.794 / 3.6) meter per sec))
= 25 mm / (3.6 x 60 / 136.794) sec
= (25 mm x 136.794) / (3.6 x 60) sec

 

[pmacias]

Sure, I'd be happy to help you understand the rate of change in millimeters per second in this scenario. First, let's define what rate of change means. Rate of change is a measure of how quickly a quantity is changing over time. In this case, we are interested in the rate at which the left rail is rising relative to the right rail.

To calculate the rate of change, we need to determine the change in the left rail's height over a given time interval. We know that the left rail rises by 25mm over a distance of 60m. However, the question asks for the rate of change in millimeters per second, so we need to convert the distance to seconds.

To do this, we use the formula speed = distance/time. In this case, the speed is given as 136.794kph (kilometers per hour). We need to convert this to meters per second, which is a more commonly used unit for speed in scientific calculations. To do this, we divide 136.794 by 3.6 (since there are 3,600 seconds in an hour) to get the speed in meters per second, which is approximately 37.998 meters per second.

Now, we can use the formula for rate of change, which is change in quantity/change in time. In this case, the change in quantity is 25mm and the change in time is the distance in meters divided by the speed in meters per second. This gives us (25mm * 37.998m/s) / 60m = 25mm * 0.6333s/m = 15.83mm/s.

So, the rate of change in millimeters per second is 15.83mm/s. The 3.6 in the original formula comes from the conversion factor between kilometers per hour and meters per second. And we multiply 25mm by the speed in meters per second to convert the distance from meters to millimeters.

I hope this helps clarify the calculations for you. Let me know if you have any further questions.